Multi-objective optimization of multilayer graphene-sheet NEMS microphones using NSGA-III and Mahalanobis distance

Abstract

This study proposes a robust multi-objective optimization framework for multilayer graphene sheet (MLGS)-based nanoscale electromechanical system (NEMS) microphones. A design optimization problem is formulated to find the optimum dimensions of the diaphragm and gap distance for three objective functions: maximum pull-in voltage, resonance frequency and sensitivity of the Microphone. To accurately capture the nonlinear behavior of the circular MLGS diaphragm, Eringen’s nonlocal plate theory is employed in conjunction with interlayer shear effects, while also accounting for electrostatic and Casimir forces. To navigate the resulting complex and non-convex three-dimensional design space, the Non-dominated Sorting Genetic Algorithm III (NSGA-III) is adopted. Furthermore, the Mahalanobis distance method is integrated with NSGA-III to improve solution diversity and guide the search toward a well-distributed Pareto front. A decision-making scheme based on Mahalanobis distance is employed to identify the most jointly improved point on the Pareto front, providing a practical and balanced optimal design solution. The proposed framework offers a comprehensive and effective strategy for optimizing the performance of NEMS microphones, particularly in the context of nanoscale sensing applications where trade-offs among competing objectives are critical.